The group of rigid motions is considered to guide the search for a natural system of space-time coordinates in General Relativity. This search leads us to a natural extension of the space-times that support Painlevé–Gullstrand synchronization. As an interesting example, here we describe a system of rigid coordinates for the cross mode of gravitational linear plane waves.

We extend a method for color weak compensation based on the criterion of preservation of subjective color differences between color normal and color weak observers presented in [2]. We introduce a new algorithm for color weak compensation using local affine maps between color spaces of color normal and color weak observers. We show how to estimate the local affine map and how to determine corre...

Recently, there has been an immense amount of challenge devoted to the subject of noncommutative space-time. Although, the idea of noncommutating space-time coordinates is an old proposal [1], the recent discoveries in string/M theories were the main source of renewed interests in the subject [2]. In particular, much work is dedicated to study the noncommutative version of the quantum field the...

dS 4,1 spacetime, projective embedded coordinates and associated isometry groups Abstract This work is intended to investigate the de Sitter metric and to give another description of the hyperbolical embedding standard formalism of the de Sitter space-time in a pseudoeu-clidean space-time E 4,1. Classical results in this mathematical formulation are reviewed in a more general setting together w...

We treat the events determined by a quantum physical state in a non-commutative space-time, generalizing the analogous treatment in the usual Minkowski space-time based on positive-operator-valued measures (POVMs). We consider in detail the model proposed by Sny-der in 1947 and we calculate the POVMs defined on the real line that describe the measurement of a single coordinate. The approximate ...

We prove an exponential estimate for the asymptotics of Bergman kernels of a positive line bundle under hypotheses of bounded geometry. We give further Bergman kernel proofs of complex geometry results, such as separation of points, existence of local coordinates and holomorphic convexity by sections of positive line bundles.